Vector Decomposition and Addition


Part 1. A car is driving down the highway at 30 m/s. Out of a single thundercloud, a raindrop falls straight downward at 40 m/s. The raindrop strikes the side window of the car skimming from one edge of the glass to the other.

Q1: Ignore the effect of drag, gravity and surface tension. Sketch this situation.

Q2: What is the velocity (speed and angle) of the raindrop as it moves across the glass? Describe this mathematically and in your own words.

Part 2. There are three ropes suspending a metal ring in the air. The ring is positioned horizontally over a flat surface, but is not in contact with the surface. Shown below is a view of the ring from above. Two forces, Fa and Fb are specified below. One additional force, Fc, has not been shown.

Fa has a magnitude of 7 N, 23o above the positive x-axis.
Fb has a magnitude of 11 N, 40o below the positive x-axis.

Q3: Determine the magnitude and direction of Fc such that the ring stays stationary. Ignore the force of gravity.

Q4: Sketch all three forces, and describe them in your own words.



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